Scott Boras’s Tall Tale
With Albert Pujols off the free agent board, Prince Fielder finds himself next in line to an immense pay day. Although Fielder hasn’t put up quite the numbers Pujols has, his accomplishments to date, at age 27, are nothing short of spectacular. He is the type of player that can immediately impact a line-up in a profound way, but questions of how he’ll age, remain. The main issue with Fielder is his weight, but this past week super-agent Scott Boras brought up a new component of Fielder’s body-type;
“Everyone talks to me about Prince’s body, but when you have that 5’11” strike zone, that is a huge advantage and that’s why that on-base percentage is sitting there. Those pitchers have to put the ball into a smaller window and I believe that it’s more difficult to do.” – Scott Boras
On the surface, this argument makes sense. Smaller players have smaller strike zones, so it follows that smaller strike zones would imply more balls, more walks, and higher on base percentage. At 5-11, Fielder is not short (I would kill to be 5-11), but he is below league average. The average height in my dataset (2006-2011 players with at least 400 Pas) is 6’1”. My first step was to plot height against BB%. I think it is fair to assume that the OBP advantage that a short player may have would be derived from walks.
While the model doesn’t tightly fit the data (R^2=5.5%), the slope is not trivial and is significantly upward sloping. Part of the low R^2 can be attributed to fact that height is measured in inches and not something more granular. Additionally, it is worth noting that is my experience, the height measurements are not the most reliable. It is clear from the plot above, and the regression analysis, that Boras is incorrect. Shorter players do not have higher BB%, in fact, they have lower BB%. Part of the problem with this simplistic analysis is there may be a lurking variable at play, namely weight. There is a strong correlation between weight and height, and what we may be seeing in the plot above is the correlation between weight and BB%. This makes more sense, because heavier players are on average stronger and thus more powerful, and we know that more power means more BBs.
If we instead plot BB% against weight we get a similar graph:
Again, the slope is significantly positive, and this fit is better, and the p-value of the slope is lower (meaning more significant).
The next step is to control for weight. We can do this by first regressing BB% on Weight, and looking at the residuals (BB%-Res). BB%-Res is the component of BB% that is not explained by Weight. Next we regress Height on Weight and take the residuals Ht-Res. Ht-Res is the component of Height not explained by Weight. Finally, we regress BB%-Res on Ht-Res. In doing this, Weight is no longer a lurking variable.
Here we see that there is a statistically significant positive relationship between BB% and height when controlling for weight.
It is now clear, that Mr. Boras is not only incorrect in asserting that shorter players have an obp% advantage due to their height, but even after controlling for weight, the exact opposite relationship exists. This should not discount Fielder’s value, but I think we can throw away the notion that shorter players have higher BB% (or OBP), because of a smaller strike zone. It is unclear why taller players have an advantage (small, but statistically significant), and I would be interested to hear your theories.
Without normalizing for power, I don’t think these results are very complete.
I would guess that larger players also hit for more power, which is also correlated for BB% (higher r^2 than height).
My thoughts exactly.
Uh, unless i’m completely mistaken, isn’t the height graph showing that TALLER players draw more walks?
The squiggles above and below the graph say just this.
Scott “Abraham Lincoln” Boras telling a lie? NEVER
George Washington?
Yes, we all know about “Honest George”
They are both famous for their honesty. According to the myth GW confessed to chopping down a cherry tree and in the confession said, “I cannot tell a lie.” And, yes, Abe has the “honest” moniker.
Honest Abe!
let’s just pretend it was a Super Troopers reference
It’s not a lie if he’s honestly mistaken. A LOT of people make the same comments.
But given Scott Boras’ carefully calculated personal mystique of being Captain Statistics, the dude who rents supercomputers, this might be showing too much credulity.
I would presume that shorter players do not hit as well as taller players. They certainly will not hit with as much power, Joe Morgan, Jimmy Wynn, and Mel Ott notwithstanding.
In fact, Morgan, Wynn, and Ott drew a ton of walks. So perhaps a players of comparable ability should be compared, rather than putting the likes of Juan Pierre and David Eckstein up against Albert Pujols and Jim Thome.
Actually, Bill James has written about this “bodytype” before, and basically when someone has it … they’re good.
Kirby Puckett, Yogi Berra, Hack Wilson, Matt Stairs, etc.
Essentially, this bodytype provides great benefits.
1. Shorter arms, quicker bat speed.
2. Shorter arms equals better coverage inside (can keep arms closer to the body).
3. Usually large powerful thighs and hips to generate power.
4. Smaller strike zone.
That’s basically every advantage a hitter can have, and I’ve basically described modern versions of Edgar Martinez and Albert Pujols.
The problem is that most short guys don’t fit this description. There aren’t many “fireplugs” or “bowling balls” or whatever description you’d use to describe a short, squat, powerful player. Most dudes are just short and slight and offer no real reason to pitch around them. They also often lack range and arm strength to be a defensive asset.
Scouts generally don’t like these guys because they don’t fit the model. But, when these guys do get a chance they are generally talented enough to make the risk worth taking.
I think that’s a classic example of selection bias… the short fatties can only become MLB players if they are immensely talented.
That wasn’t selection bias, that was THE point. The only way these guys actually make it to majors is to by being very good.
In other words short and talented is better than tall and average.
My point was that these types have serious batting advantages.
That shorter players will have less power is an incorrect assumption. Look at the players with over 500 career HRs. 6 ft and under members include Aaron, Mays, Mantle, Killebrew, Sosa, Palmeiro, Foxx, Jackson, Ramirez, Ott, Sheffield. Add the players who were listed as 601 (which might have been in spikes with a bit of exaggeration in many cases) and you have over half the 500 HR club.
The 3000 hit club is overwhelmingly short statured, even the modern (post 1980) players: Bagwell, Biggio, Molitor, Yount, Gwynn, Pucket, Ichiro, etc. And then you have the average size players who made themselves small by hitting out of some form of a crouch, like Brett, Boggs, et al.
One of the reasons that the argument that baseball will lose prospects to football and basketball unless they pay large signing bonuses is so specious is that it ignores the reality that short works in baseball like no other sport–except for maybe cricket. The big athletes in basketball and football are generally at a disadvantage in baseball.
When did Bagwell, Puckett, and Ichiro join the 3000 hit club?
Another possible factor: while the batter’s height should change the strike zone up and down, the umpires are probably used to calling strikes for the average batter. That is, they really don’t change their strike zone that much even if the batter is 3″ shorter or taller than the average.
That is correct. The strike zone size as called by the umpires changes very little depending on the height of the player. I found that the vertical extent of the zone increases, on average, by 0.3 inches for a batter four inches taller than average.
http://www.baseballprospectus.com/article.php?articleid=14098
My theory…Boras is still full of sh*t.
Yes, but GMs and owners will continue to let Boras shit in their mouths and thank him for it.
Anyone who could persuade a GM to offer Willie Bloomquist a two-year contract for $3.8 million shortly after humiliating the same GM in the press has an absurd power to persuade. Despots across the earth are envious. Frat boys armed with roofies in a college bar have a lower probability to score.
What if you replace BB% in those plots with ISO?
I’m pretty sure this is NOT the way to do multivariate regression with correlated regressors…
multicollinearity?
It IS if you want to control for a variable. I can’t link you the textbook, but this should suffice,
http://en.wikipedia.org/wiki/Partial_correlation#Using_linear_regression
Good Lord, Noah. The whoosh you just heard was the point, flying far over your head.
Boras didn’t make it explicit, but the idea is that players WHO HAVE THE POWER TO MAKE IT COUNT gain an added advantage by providing a smaller strike zone. It allows that slugger to key into a smaller area.
Another note: It’s harder to get the ball down against a short slugger, heightening the risk of home runs. A knee-high heater to Ryan Howard is thigh-high to Fielder, and you’re in trouble if you go there.
Wow. Good Lord is right.
Read Boras’ quote. Please.
He says explicitly that Fielder’s height is the reason he has a high OBP. He also says pitchers are “trying” to put a ball in a smaller area… not miss it.
I don’t think that’s the idea Boras is trying to get across at all. I think it really is just as simple as it sounds. No GM will buy that argument, but that is what Boras is saying. Also, you say that it’s harder to keep the ball down against shorter players, so shorter players will see more balls in the zone. I’d like to see your numbers supporting this. From what I’ve seen of baseball, this doesn’t seem to be true, short players hit for less power in general, but I haven’t done the research, so I’m interested in seeing yours. Eckstein is tiny, but he doesn’t hit for power. Of course, that could just be because he’s short
More specifically the foot to knee segment of the body makes up a small portion of total height. This is a WAG, but for every inch of additional knee height, a person has to probably grow 5 inches (or more). That’s a lot of height and very little change in the lower bound of the strike zone.
Now…mix that in with what Mike Fast found – every 4 inches of height increases the strike zone by only .3 inches.
I agree with Matt TrueBlood’s sentiment. Scott Boras wasn’t explicitly making a statement about shorter players.
Objectively True Statement: The fact that Prince Fielder chances of drawing a walk increase because he is shorter. (Or Rather, Prince Fielder has a greater chance at getting walked at his height rather than if he was taller).
Similar ground covered here:
http://www.fangraphs.com/blogs/index.php/the-next-market-inefficiencies-little-people-in-baseball/
Shorter players have a harder time covering the entire plate?
Do I want Prince Fielder trying to cover to low and away part of the plate?
No, I want him looking middle in at pitches he can crush and let everything else go. If a pitcher paints the 3-zone with 3 pitches, we’ll tip our cap and head back to the dugout, with the realization that most pitchers using that approach are going to walk him more times than they’ll K him, and just as many guys are eventually going to leave something in the wrong spot.
See Jose Bautista for this can work extremely well.
Batters usually cover the outer half with body tilt, not arm extension. A pitcher wants batters to reach the outside corner pitch by straightening their arms, that’s weak contact.
Carlos Delgado driving a low/away pitch via body tilt:
http://www.chrisoleary.com/projects/Baseball/Hitting/Images/Hitters/CarlosDelgado_HomeRun_005.jpg
A tller player may have more “reach” via tilt to an outside pitch, but also takes longer time getting there. As a hitter what do you want most? [1] reach or [2] quicker getting there. The answer is #2.
Scott Boras is 100% correct here.
No he isn’t.
Do some reading and find out who Eddie Gaedel is before you disagree. It was actually a funny post.
I thought the fact that he replied as “Randy Johnson” indicated he understood the joke…?
So Matt did the very thing he accused the poster above him of doing? How funny!
Come now, Matt. You’re just jealous of my career as a successful NFL sideline photographer.
Taller players have a better vantage point?
Do NL pitchers tend to be taller than the average MLBer? Because getting rid of the above-average height and below-average OBP by pitchers would, I think, only strengthen the correlation.
As for a reason why this phenomenon occurs, I suggest player morale. After all:
Short people have no reason
Short people have no reason
Short people have no reason to liiiiiiiiiiive
Well that’s a brilliant reference. And it’s also quite fitting given that this series attacking Prince Fielder is really getting (unintentionally) close to outright prejudice.
If the analyses claiming that his fatness or shortness were even close to fundamentally correct, this would not be so. But at this point it’s really just namecalling with a bunch of colory charts.
This analysis is a bit of a mess for me. I’m not sure if we’re just simply trying to disprove Boras’ words or if we’re actually asserting what you asserted at the bottom.
I thoroughly enjoy “Ah! Neat!” articles, but you’re coming very, very close to the line where there’s enough math in the article to necessitate the math be done properly and formally.
Anyways, I’d be interested to see the graph of simply Zone% or 1-(Zone%) versus height. Obviously we’re going to be in the same spot, but I would be curious none the less because, as I said, I enjoy “ah! neat!” articles.
“Necessitate the math be done properly and formally”? I take no offense to this comment, because it is my intention to provide you with sound analysis. Could you be more specific when you say that the math was done incorrectly/informally? I took the partial correlation of BB% and Height, with Weight being removed. I’m pretty sure all the math is sound, and it didn’t make sense to provide you with residual analysis or p-values for all the correlations. I think it suffices to say that the slope is significant, but if there is information you would like that is not there, please let me know.
It’s not that the math was done incorrectly, it’s that the selection of variables leads to a poor application of that math. The ability to hit for power is not explicitly included in the model and a lot of the noise comes from this missing variable. Just looking at top 200 PA guys in MLB last year (402 PA or more) and breaking them into quartiles:
Upper: 63.7BB/600PA, 55.7 per 600 excluding IBB
Second: 53.4 and 49.0
Third: 45.5 and 41.8
Last: 43.8 and 41.0
Taller and bigger players tend to dominate the first two quartiles, but not all tall/big guys hit for power and not all small/short players don’t either.
Speed is another factor. If a big slow, power hitting guy comes up with 2 outs, I’m going to pitch around him…especially if a substantially weaker batter follows. He has a greater probability of being walked if I you don’t give him anything to hit, but I might get him on some tough pitches too.
If someone wants to quantify Fielder’s ability to draw walks based upon height, run a regression on non-IBB rates vs. ISO and some measure of speed ( SB/(1B+BB) or (SB/(1B+2B+BB) ) for the last 5 years compared to league average non-intentional BB rates. The r-squared should be substantially higher. Look at the error terms and tell me if there’s anything significant about Fielder’s BB rates then. I suspect they don’t look all that abnormal. Even if he is drawing walks at a higher than expected rate, you’d have to question how much of that is a good batting eye vs. height., batting order protection, etc.
Doing what you’ve done would be like running a similar analysis on NYC subway ridership from 6-9am every day of the week and concluding that Saturday isn’t a busy day simply because it’s Saturday…not because relatively fewer people go to work on Saturday morning.
Very nice analysis…takes me back to an econometrics class I once took.
It would be difficult to completely rule out weight as a factor since a major component of weight is muscle mass. While muscle mass does not a walk make, it could help to categorize people into light tall and strong tall etc., the difference between perhaps, Jason Werth and someone I cant think of right now that is tall and thin and less likely to hit the ball hard on a regular basis.
Walks have more to do with how a pitcher approaches the batter than the physical strike zone itself, although I understand the irony in such a statement. Think of the ol’ 2-strike, getting the batter to chase a high fastball pitch – like Rivera is so famous for. He routinely stayed away from the strike zone. I would think even more so on a dangerous hitter like Fielder.
Perhaps even, we could include an immeasurable factor such as perception or fear. If a taller batter can cover more area of the plate with strength (A-Rod), then the farther away from the strike zone a pitcher will stay.
Fielder simply has “Tall” characteristics, meaning he crushes HRs like we would expect from a tall-body type player and is capable of covering a large pert of the strike zone with that power.
Basically the point is if a pitcher cant pitch to the outside of the zone without feeling like the batter is capable of hurting them, then the pitcher is more likely to walk the batter. Think of a player like Miguel Tejada. No one regularly pitched inside on him because he wasn’t a very good outside pitch hitter, even though he was moderately tall and had power. Fielder, while not tall, could do 10 times what Tejada could with the same outside pitch, and therefore, more walk-able. Not very statistical but if you performed the same analysis you did between weight and walks with, say, Height and LD%(line-drive %) or some other variable that would measure height and performance, we could attribute importance to height. If we could determine that height and power or height and IP%(in-play %) are significant and show that height is a factor in how effective a batter is (walk-able), then we could also do the same for weight.
If after this we find that the outliers, such as small heavy players, are belting line-drives, then we can say they are capable of covering the plate well and we could then compare those players to BB%.
Ultimately Im trying to say that plate coverage, which MAY be more typical in larger hitters, is more likely to influence walks than height alone. Then again I have no evidence to back it up:)
Doesn’t look like a statistically significant correlation in that last graph to me.
It is. The p-value of the slope is .001, so it is VERY significant. .001 means that there is a 1/1000 chance that you would see that slope by pure chance.
Regression probably isn’t your ideal tool for this. The low r^2 should tip you off that you have a very cruddy model.
low r^2 means that it is a poor predictive model, NOT that that the model is insignificant.
In any academic setting if higher order adjustments could not improve the model, you’d just stand on summary stats. There are very few cases where analysis relying on a 5.5 r2 would not be laughable, and actually I know people who would be very angry with the attempt. This is so bad.
Paul, I’m sorry you feel this way, but I do believe that the model above clearly shows that being short does not improve your OBP. You could argue that with such a low r^2 all you’re seeing is noise, which is fine, because that would still discount Boras’s comments.
Noah,
Not to get on you unfairly, as someone with somewhat weaker regression skills than you, I understand that this is challenging work. But wouldn’t you HAVE to argue that all you’re seeing is almost certainly noise? A model with an R^2 of .055 is more aptly described as a scatter plot.
To your comment a couple posts above, what’s it matter if the P-Value of the slope of the fitted line is significant if that line is for all intents and purposes horizontal? If I’m reading this right, 5 inches of height equals less than a 1% increase in walks when controlling for weight.
Let’s assume it is all noise, the point still holds – Shorter players do NOT enjoy a BB% advantage, at the very best there is no relationship.
Better, I can agree with that.
I dont remenber when, I dont remenber whom, but someone over at THT tried to answer this same question
One more reason for a standardized strike zone, judged by camera/computers.
Tall people shouldn’t have to cover a larger strike zone.
Short people shouldn’t get a smaller zone.
Rule 2.00: The Strike Zone
The STRIKE ZONE is that area over home plate the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the hollow beneath the kneecap. The Strike Zone shall be determined from the batter’s stance as the batter is prepared to swing at a pitched ball.
By Rule, short people should get a smaller zone.
I completely disagree. Taller people should have a bigger zone.
Could it be that shorter people often make it to the majors for reasons other than their hitting skills, (defense, speed…) and thus teams are okay with getting a lower BB% and less offensive production because they derive it elsewhere from these guys? While the larger players (this is certainly true with weight, possibly with height as well) who don’t have high BB% simply lack the skill set to make up for a diminished offensive performance and never make it to the big leagues in the first place? Ex. Jack Cust vs. Carlos Peguero…
This makes sense to me. Smaller body types often break in well as defensive specialists.
Is ISO correlated with height? Could you use it as an IV?
I really don’t see how height would make that much if any difference in the strike zone in 99% of the cases. Now if you are 5’6 or 6’6 maybe but if you’re between 6’3 and 5’11 I think the difference would be miniscule because all that really matters is the length from your knees to about your abs since that’s where the strike zones at for most umps. And I’m no Doctor but I’d imagine that span isn’t that much if any longer for a 6’3 person than a 5’11 person.
IMO, the height of batters is largely irrelevant until you can account for the variations in the crouch at the plate. A player may be 6’1″ (average) and have a smaller strike zone due to his crouch, while a shorter batter with a more upright approach can have a larger zone.
That works to a point, but what about shorter than average players who crouch? Jeff Bagwell (6’0″) and Rickey Henderson (5’10”) are key example there. Both took tons of walks and had power.
There seems to me to be very little if any linear relationship between height and walk percentage, so… why use a linear regression model? Why not simply split up batters by “tall”, “short”, and, uh,…, “regular” and see if there’s a difference in walk percentages among these groups?
I did, but didn’t post it, because the regression told the story. I ran an ANOVA with shorter (below average) and taller (above average), and my findings were exactly the same – Taller players have a higher BB% than shorter players at a statistically significant level.
Pity you didn’t post it, because that would be far more convincing to me.
This study can be done in a much better way. The suggestion by Boras is that umpires call a smaller strike zone for smaller players. The null hypothesis, then, is that umpires call the same strikezone regardless of player.
Since you have pitch fx data, there is no reason to try to test the hypothesis indirectly by looking at correlates of strike zone (walks). Look at the strike zone directly. To test the hypothesis simply calculate the average euclidean distance from the centroid for all called strikes and compare that to stature.
My guess is that there is no relationship between stature and how umpires call the game. I don’t think umpires are that precise honestly. ….I also had to chuckle at the suggestion that a more fine grained stature estimate than inches might improve the correlation. How good must you think the umpires are!!!!!
You are correct.
I provided a link to my study of PITCHf/x strike zone data in a previous comment.
Ah, well done. ….I should get in the habit of reading the comments before commenting.
When they said “baseball is a game of inches,” I don’t think this is what they had in mind…
If Prince Fielder is 5’11” then I’m Captain Jack Sparrow
YEEEEE-AAARRRRRRRRRR ME MATEY!
OBP% is redundant. LikE ATM MACHINE
I’m not sure what the point is of normalizing for weight.
What I am sure of is that you need to throw skill position players out of the study. A shortstop is going to be both shorter than average and also a low-walk guy, but for reasons that probably don’t diminish the claim as pertains to Prince Fielder.
“Part of the low R^2 can be attributed to fact that height is measured in inches and not something more granular.”
An the US is one of only a few countries not on the metric system, which would provide better granularity, as there are 2.54 centimeters to the inch. (Mind you, up here in Canada, most people still know their height in feet and inches but not in centimeters.)
Let’s assume Scotty Boras is correct. Why does it even matter? I could see how it would matter for a prospect as you’re trying to project how he’d fare at the MLB level. But if Fielder has an advantage from his height, it’s already reflected in his performance over the last several years. It’s not new information.
This is probably the best comment on the board.
I have a problem using only BB% in your analysis. I get why you did it, but I don’t think it comes close to addressing the main point. Do shorter players have an advantage with their small K Zone?
Take Altuve for example. He doesn’t walk much, but this is a result of his hack at anything approach. What you do see is that he hardly strikes out. Looking at his minor numbers his K% looking is almost non-existent. This would lend me to believe it is harder for pitchers to strike him out becuase of his size.
I think in order to really analyze if size is an advantage, you should check out K% looking instead of BB%. I feel a short player has the advantage covering his strike zone. Whether that translates to good production, well that’s up to the individual player’s talent level.
But in the OBP case, shouldn’t you use OBP instead of BB% to see if shorter players have an OBP advantage? I get the correlation argument with BB%, but it still doesn’t make sense to argue against Boras’s statement of OBP based on a different metric. Start out simple, compare OBP against heights and see what happens.